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- 3) Let D = {(x, y) E R² | 0 < x² + y² < 4}. Give all boundary points of D. Is D open, closed or bounded? Justify all your answers. The definition of open set is in your Ebook in section 13.2. The related definitions of closed and bounded set are as follows: Closed: A set D is closed if it contains all of its boundary points. Bounded: A subset D of IR" is bounded if it is contained in some open ball D,(0). For example the interval [-1,5) is neither open nor closed since it contains some but not all of its endpoints. It is bounded since it is contained in the open interval D6 (0)=(-6,6).6. Show that is an open subset of R². R² – Z²5. If X any Y are sets, then X-Y = {€X:z4Y} If X is open set and Y is closed set. Prove that (a) X-Y is open.
- Show the following set is convex. x10 Determine a-cut sets of the above set for a=0.5, 0.8 and 0.9.9. Let {Aa: a E I} be an indexed family of sets and let B be a set. Prove: (Uael Aa) nB = Uael( Aan B)10. The set {0} in the indiscrete space X is A.open but not closed B.closed but not open C.both open and closed D.neither open nor closed
- 1. show that if S, and S, are definite sets with S-n and S-m, then |S, YS,3. Consider the sets A = {0, 1} Which is the following statements is TRUE? (a) 0 EAN B (b) 0 € An B (c) {0,1} CANB (d) All of the other statements are false. and B = {CC is a subset of {0, 1}}.6. if x C y. (a) (b) Let R = {a: a is a cut}.Let x, y, R. We say that aRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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